Scheduled Real Fn
Scheduled Real Fn is a direct subtype of Timed Real To Real Function
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with functions Scheduled Real Fn Functions, keys Scheduled Real Fn keys and example object SchedRealFn
TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE Scheduled Real Fn
This type represents a function ƒ that maps a sequence d , x₁ , x₂ , ... , xᵤ consisting of any allowed date d followed by u real variables (i.e. single numbers) x₁ , x₂ , ... , xᵤ into v real variables y₁ , y₂ , ... , yᵥ and constructed (see details below) with the help of a special function 𝘨 and r functions ƒ₁ , ƒ₂ , ... , ƒᵣ, each of which maps the same u real variables x₁ , x₂ , ... , xᵤ into v real variables y₁ , y₂ , ... , yᵥ.
Schematically:
ƒ: (d , x₁, x₂, ... , xᵤ) → (y₁ , y₂ , ... , yᵥ)
where d is date and all other variables are numbers.
The functions ƒ₁ , ƒ₂ , ... , ƒᵣ are expected to be objects of which the type is a subtype of Real To Real Function
The date d is generally allowed only if it belongs to the set of dates implied by the Schedule object defined through the key Schedule
There exist two cases regarding the specification of the Schedule object defined through the key Schedule
Case 1: The Schedule object is specified.
Then that object implies a sequence of n dates d₁ , d₂ , ... , dₙ, with n not necessarily the same with the number of functions r.
If d ∉ d₁ , d₂ , ... , dₙ, the special function 𝘨 alone produces the final result, provided that function is defined, with an error issued on a different occasion.
Otherwise, a correspondence is established between the dates d₁ , d₂ , ... , dₙ and the functions ƒ₁ , ƒ₂ , ... , ƒᵣ so that d₁ corresponds to ƒ₁, d₂ to ƒ₂ and so on.
If there exist more dates than functions, i.e. if n > r, all non-paired dates are forced to correspond to the last function ƒᵣ
Formally: If n > r then dᵢ → ƒᵣ for all i > r
If there exist fewer dates than functions, i.e. if n < r, all non-paired functions beyond the ƒₙ are ignored.
Formally: If n < r then ƒᵢ is ignored for all i > n
Case 2: The Schedule object is not specified.
In this trivial case, the function 𝘨 must be defined since it is solely responsible for the final result, while the functions ƒ₁ , ƒ₂ , ... , ƒᵣ are all ignored.